Analysis of Bessel Beam Generation Using MetaMaterials in Photonic Integrated Circuits

Abstract

Bessel beams, known for their unique non-diffracting property, maintain their shape and intensity over long distances, making them invaluable for applications in optical trapping, imaging, and communications. This work presents a comprehensive theoretical analysis of micro-photonic antennas designed to generate Bessel beams within the Terahertz (THz) and optical frequency ranges. The technique is demonstrated by generating far-field patterns of Bessel waves at these frequencies. The design employs metasurface patterns arranged as arrays of concentric rings atop rectangular silicon waveguides, collectively creating a Bessel beam. Dyadic Green's function integral equation techniques are used to model the transverse electric (TE) and transverse magnetic (TM) fields in the metasurface radiation zone. Utilizing orthogonal vector wave functions, Bloch theorem, Floquet harmonics, and the transverse resonance technique, a photonic chip is designed to achieve a non-diffracting range of 500 $\mu$m at the optical telecom wavelength of 1.5 $\mu$m for a metasurface radius of 25 $\mu$m. A radiation efficiency exceeding 80$\%$ is achieved by optimizing the attenuation constant ($\alpha$) along the structure. The theoretical models are validated through simulations for both optical (1.5$\mu$m) and Terahertz (14 $\mu$m) wavelengths, demonstrating significant alignment between predictions and simulation results.